Work and Power Calculator
Solve work done by a force at any angle, power from work and time or from force and speed, and efficiency from output and input — for any unknown, in any units. Results come with the working and with the same power in watts, kilowatts and horsepower (mechanical, metric and electrical), or the same energy in joules, kWh and kcal. Runs in your browser; free, no sign-up.
Work is force times the distance moved in the direction of the force. θ is the angle between the force and the motion: 0° pushes along the motion (positive work), 90° does no work, 180° opposes the motion (negative work).
Calculated
Between 0° and 180°.
Results
433 J
Work W
The working
- Start from W = F × d × cos(θ).
- W = 50 × 10 × cos(30°) = 433 J
The same value in other units
| Unit | Value |
|---|---|
| J | 433 |
| kJ | 0.433 |
| kcal | 0.1035 |
| Wh | 0.1203 |
| kWh | 1.203 × 10⁻⁴ |
| ft·lbf | 319.4 |
Assumes a constant force along a straight path. For a force that varies, work is the area under its force–distance graph.
How to Use the Work and Power Calculator
- 1. Pick the calculation. Work for a force acting over a distance, Power from work and time, Power from force and speed, or Efficiency for the useful share of an energy or power input.
- 2. Choose the unknown and fill in the rest. The box you solve for becomes the answer. Angles can be in degrees or radians; power can be in watts, kilowatts or any horsepower.
- 3. Read the working. The equation, its rearrangement and the substituted numbers are shown, with any unit conversions.
- 4. Use the equivalents. Power appears in W, kW, hp, PS and electrical hp; energy in J, kJ, kcal, Wh, kWh and ft·lbf. Efficiency shows what is lost.
The Formulas
| Quantity | Formula | Unit |
|---|---|---|
| Work by a constant force | W = F d cos θ | joule (J) = N·m |
| Average power | P = W ÷ t | watt (W) = J/s |
| Power of a force on a moving object | P = F v cos θ | watt (W) |
| Efficiency | η = useful output ÷ total input | a fraction, or a percentage |
Reference: OpenStax University Physics, Volume 1, sections 7.1 and 7.4. θ is the angle between the force and the displacement (or velocity).
Only the part of the force along the motion does work. At θ = 0° all of it counts; at 90° none does, which is why carrying a bag at constant height across a room does no work on the bag; and beyond 90° the work is negative, as when friction opposes the motion.
Worked Examples
Work. Pull a crate with 50 N for 10 m, with the rope at 30° above the ground. W = 50 × 10 × cos 30° = 433 J (the calculator's default). Only 433 J of the 500 N·m of force-times-distance does work along the floor.
Power from work and time. A winch lifts a load, doing 36 kJ of work in 30 s: P = 36,000 ÷ 30 = 1,200 W = 1.2 kW, which is 1.609 mechanical horsepower. Run for an hour, that is 1.2 kWh of energy.
Power from force and speed. A car whose wheels push the road with 2,000 N at a steady 15 m/s delivers P = 2000 × 15 = 30,000 W = 30 kW = 40.23 hp.
Efficiency. A motor takes in 800 J and delivers 600 J of useful work: η = 600 ÷ 800 = 75%. The other 200 J, 25%, is lost, mostly as heat.
Watts and Horsepower
| Unit | Value in watts | Definition |
|---|---|---|
| Mechanical horsepower (hp) | 745.6999 | 550 foot-pounds-force per second |
| Metric horsepower (PS, CV) | 735.49875 | 75 kilogram-force metres per second |
| Electrical horsepower | 746 (exact) | Used for electric motor ratings in North America |
Source: NIST Special Publication 811, Appendix B.8. One kilowatt is about 1.341 mechanical horsepower.
Common Mistakes
- Confusing work and power. Work is the total energy transferred; power is how fast. Lifting a box slowly or quickly takes the same work but very different power.
- Treating the kilowatt-hour as power. A kWh is energy: 3.6 million joules, the energy of 1 kW for one hour.
- Using the wrong force when lifting. To lift an object at constant speed, the force equals its weight, mg; the Force Calculator gives it.
- Forgetting the angle. A force at an angle to the motion does less work than its full size suggests.
Frequently Asked Questions
- What is the formula for work?
- W = F d cos θ for a constant force F acting over a displacement d, with θ the angle between them. When the force is along the motion, it simplifies to W = Fd. The unit is the joule, 1 N·m.
- What is the formula for power?
- Average power is work divided by time, P = W ÷ t. For a force acting on an object moving at speed v, P = F v cos θ. The unit is the watt: 1 W is 1 J per second.
- How many watts are in a horsepower?
- One mechanical horsepower is 745.7 W (550 ft·lbf/s). A metric horsepower is 735.5 W and an electrical horsepower is exactly 746 W. The calculator lists a power in all three so you can match whichever rating you are given.
- Why is no work done when you carry a bag across a room?
- Because the force you exert is upward, perpendicular to the horizontal motion, so cos 90° = 0. You still get tired because your muscles use energy to hold the force, but no work is done on the bag.
- Can efficiency be 100% or more?
- No real machine reaches 100%, and none can exceed it, since that would create energy. Friction, heat and sound always take a share. The calculator rejects efficiencies above 100%.
- Is a kilowatt-hour a unit of power or energy?
- Energy. A kilowatt-hour is the energy used by 1 kW running for one hour, which equals 3.6 × 10⁶ J. Your electricity bill charges for energy in kWh, not power in kW.